What is the general solution for cos(4x)cos(x)+sin(4x)sin(x)= 1/2 ?

The general solution for cos(4x)cos(x)+sin(4x)sin(x)= 1/2 is x= pi/9+(2pin)/3 ,x=(5pi)/9+(2pin)/3

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cos(4x)cos(x)+sin(4x)sin(x)= 1/2

cos (4 x) cos (x) + sin (4 x) sin (x) = \frac{1}{2}

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{5 π}{9} + \frac{2 πn}{3}

Solution steps

cos (4 x) cos (x) + sin (4 x) sin (x) = \frac{1}{2}

Rewrite using trig identities

cos (4 x - x) = \frac{1}{2}

General solutions for

cos (4 x - x) = \frac{1}{2}

4 x - x = \frac{π}{3} + 2 πn, 4 x - x = \frac{5 π}{3} + 2 πn

Solve

4 x - x = \frac{π}{3} + 2 πn : x = \frac{π}{9} + \frac{2 πn}{3}

Solve

4 x - x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{9} + \frac{2 πn}{3}

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{5 π}{9} + \frac{2 πn}{3}

- 4 sin^{2} (θ) - 15 sin (θ) = - 7 sin (θ) - 5

tan^{2} (θ) + 7 tan (θ) + 5 = 0

tan (θ) = \frac{2 3}{1}

cos^{2} (x) - cos (x) = 0, x, 0 \leq x \leq 2 π

6 cos^{2} (x) + sin (x) - 4 = 0

What is the general solution for cos(4x)cos(x)+sin(4x)sin(x)= 1/2 ?
The general solution for cos(4x)cos(x)+sin(4x)sin(x)= 1/2 is x= pi/9+(2pin)/3 ,x=(5pi)/9+(2pin)/3